Question

AB||DC and AD||BC if DAB is 75 find the measures of a b c
give answer by step by step​

Answer 1

Given:-

AB ║ DC      and      AD ║ BC

and, ∠DAB = 75°

Solution:-

Here, AD ║ BC  and  AB is transversal

∵ Consecutive interior angles are supplementary

∴ ∠DAB + ∠ABC = 180°              [ AD ║ BC and they are Consecutive interior angles ]

so, 75° + ∠ABC = 180°

⇒ ∠ABC = 180° - 75°

⇒ ∠ABC = a = 105°

Now, AB ║ DC  and  BC is transversal

∵ Consecutive interior angles are supplementary

∴ ∠DCB + ∠ABC = 180°               [ AB ║ DC and they are Consecutive interior angles ]

so, ∠DCB + 105° = 180°

⇒ ∠DCB = 180° - 105°

⇒ ∠DCB = b = 75°

Now, AD ║ BC  and  DC is transversal

∵ Alternate interior angles are Equal in measure

∴ ∠DCB = ∠EDC             [ AD ║ BC and they are Alternate interior angles ]

⇒ ∠EDC = c = 75°

Hence, a = 105°  and  b = c = 75°

Some important terms:-

• When two parallel lines intersected by a transversal then:-

1. Alternate interior angles are equal.
2. Alternate exterior angles are equal.
3. Corresponding angles are equal.
4. Consecutive interior angles are supplementary.
5. Vertically opposite angles are equal.